Hochschild cohomology of algebras of dihedral type, I: The family $D(3\mathcal K)$ in characteristic $2$
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A. I. Generalov
Translated by: the author - St. Petersburg Math. J. 16 (2005), 961-1012
- DOI: https://doi.org/10.1090/S1061-0022-05-00886-1
- Published electronically: November 22, 2005
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Abstract:
In terms of generators and defining relations, the Hochschild cohomology algebras are described for all algebras of dihedral type in the family $D(3\mathcal {K})$ over an algebraically closed field of characteristic $2$. The results are applied to three other families of algebras of dihedral type, namely, $D(3\mathcal {A})_1$, $D(3\mathcal {B})_1$, and $D(3\mathcal {D})_1$. As a corollary, a description is obtained for the Hochschild cohomology algebra for blocks with dihedral defect group and three simple modules; in particular, this applies to principal blocks of the groups $\operatorname {PSL}(2,q)$ with odd $q$.References
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Bibliographic Information
- A. I. Generalov
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198904, Russia
- Received by editor(s): March 17, 2004
- Published electronically: November 22, 2005
- © Copyright 2005 American Mathematical Society
- Journal: St. Petersburg Math. J. 16 (2005), 961-1012
- MSC (2000): Primary 16E40
- DOI: https://doi.org/10.1090/S1061-0022-05-00886-1
- MathSciNet review: 2117449